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236
Comparing Dynamic Causal Models
 NEUROIMAGE
, 2004
"... This article describes the use of Bayes factors for comparing Dynamic Causal Models (DCMs). DCMs are used to make inferences about effective connectivity from functional Magnetic Resonance Imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, ..."
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Cited by 81 (34 self)
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This article describes the use of Bayes factors for comparing Dynamic Causal Models (DCMs). DCMs are used to make inferences about effective connectivity from functional Magnetic Resonance Imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, the connectivity pattern between the regions included in the model. Given the current lack of detailed knowledge on anatomical connectivity in the human brain, there are often considerable degrees of freedom when defining the connectional structure of DCMs. In addition, many plausible scientific hypotheses may exist about which connections are changed by experimental manipulation, and a formal procedure for directly comparing these competing hypotheses is highly desirable. In this article, we show how Bayes factors can be used to guide choices about model structure, both with regard to the intrinsic connectivity pattern and the contextual modulation of individual connections. The combined use of Bayes factors and DCM thus allows one to evaluate competing scientific theories about the architecture of largescale neural networks and the neuronal interactions that mediate perception and cognition.
The role of Occam’s Razor in knowledge discovery
 Data Mining and Knowledge Discovery
, 1999
"... Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite di ..."
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Cited by 78 (3 self)
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Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite different ways. The first interpretation (simplicity is a goal in itself) is essentially correct, but is at heart a preference for more comprehensible models. The second interpretation (simplicity leads to greater accuracy) is much more problematic. A critical review of the theoretical arguments for and against it shows that it is unfounded as a universal principle, and demonstrably false. A review of empirical evidence shows that it also fails as a practical heuristic. This article argues that its continued use in KDD risks causing significant opportunities to be missed, and should therefore be restricted to the comparatively few applications where it is appropriate. The article proposes and reviews the use of domain constraints as an alternative for avoiding overfitting, and examines possible methods for handling the accuracy–comprehensibility tradeoff.
The calculi of emergence: Computation, dynamics, and induction
 Physica D
, 1994
"... Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how modelbuilding observers infer from measurements the computational capabilities embedded ..."
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Cited by 77 (14 self)
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Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how modelbuilding observers infer from measurements the computational capabilities embedded in nonlinear processes. An observer’s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference. The discovery of structure in an environment depends more critically and subtlely, though, on how those resources are organized. The descriptive power of the observer’s chosen (or implicit) computational model class, for example, can be an overwhelming determinant in finding regularity in data. This paper presents an overview of an inductive framework — hierarchicalmachine reconstruction — in which the emergence of complexity is associated with the innovation of new computational model classes. Complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. Illustrative examples are drawn from the onset of unpredictability in nonlinear systems, finitary nondeterministic processes, and
Data Clustering: 50 Years Beyond KMeans
, 2008
"... Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and m ..."
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Cited by 75 (3 self)
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Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is exploratory in nature to find structure in data. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, Kmeans, was first published in 1955. In spite of the fact that Kmeans was proposed over 50 years ago and thousands of clustering algorithms have been published since then, Kmeans is still widely used. This speaks to the difficulty of designing a general purpose clustering algorithm and the illposed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semisupervised clustering, ensemble clustering, simultaneous feature selection, and data clustering and large scale data clustering.
Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity
 IEEE Transactions on Information Theory
, 1998
"... The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic condition un ..."
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Cited by 67 (7 self)
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The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic condition under which the ideal principle should be applied is encapsulated as the Fundamental Inequality, which in broad terms states that the principle is valid when the data are random, relative to every contemplated hypothesis and also these hypotheses are random relative to the (universal) prior. Basically, the ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized. If we restrict the model class to the finite sets then application of the ideal principle turns into Kolmogorov's mi...
Competitive online statistics
 International Statistical Review
, 1999
"... A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive online algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid’s prequential sta ..."
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Cited by 63 (10 self)
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A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive online algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid’s prequential statistics). In this approach, which we call “competitive online statistics”, it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive online statistical procedures are guaranteed to hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss. Keywords: Bayes’s rule, competitive online algorithms, linear regression, prequential statistics, worstcase analysis.
A tutorial introduction to the minimum description length principle
 in Advances in Minimum Description Length: Theory and Applications. 2005
"... ..."
Hypothesis Selection and Testing by the MDL Principle
 The Computer Journal
, 1998
"... ses where the variance is known or taken as a parameter. 1. INTRODUCTION Although the term `hypothesis' in statistics is synonymous with that of a probability `model' as an explanation of data, hypothesis testing is not quite the same problem as model selection. This is because usually a particul ..."
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Cited by 57 (3 self)
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ses where the variance is known or taken as a parameter. 1. INTRODUCTION Although the term `hypothesis' in statistics is synonymous with that of a probability `model' as an explanation of data, hypothesis testing is not quite the same problem as model selection. This is because usually a particular hypothesis, called the `null hypothesis', has already been selected as a favorite model and it will be abandoned in favor of another model only when it clearly fails to explain the currently available data. In model selection, by contrast, all the models considered are regarded on the same footing and the objective is simply to pick the one that best explains the data. For the Bayesians certain models may be favored in terms of a prior probability, but in the minimum description length (MDL) approach to be outlined below, prior knowledge of any kind is to be used in selecting the tentative models, which in the end, unlike in the Bayesians' case, can and will be fitted to data
Further Experimental Evidence against the Utility of Occam's Razor
 Journal of Artificial Intelligence Research
, 1996
"... This paper presents new experimental evidence against the utility of Occam's razor. A systematic procedure is presented for postprocessing decision trees produced by C4.5. This procedure was derived by rejecting Occam's razor and instead attending to the assumption that similar objects are likely t ..."
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Cited by 54 (5 self)
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This paper presents new experimental evidence against the utility of Occam's razor. A systematic procedure is presented for postprocessing decision trees produced by C4.5. This procedure was derived by rejecting Occam's razor and instead attending to the assumption that similar objects are likely to belong to the same class. It increases a decision tree's complexity without altering the performance of that tree on the training data from which it is inferred. The resulting more complex decision trees are demonstrated to have, on average, for a variety of common learning tasks, higher predictive accuracy than the less complex original decision trees. This result raises considerable doubt about the utility of Occam's razor as it is commonly applied in modern machine learning. 1. Introduction In the fourteenth century William of Occam stated "plurality should not be assumed without necessity". This principle has since become known as Occam's razor. Occam's razor was originally intended a...